Question

Find \(lt_{(x,y,z,w)\rightarrow(3,1,1,11)}\frac{x^4+y^2+z^2+2x^2y+2yz+2x^2z-(w)^2}{x^2+y+z-w}\)

(a) 700

(b) 701

(c) 699

(d) 22

The question was posed to me in an internship interview.

Question is taken from Limits and Derivatives of Several Variables in chapter Partial Differentiation of Engineering Mathematics

Answer 1

Right answer is (d) 22

Easy explanation: Simplifying the expression we have

\(lt_{(x,y,z,w)\rightarrow(3,1,1,11)}\frac{(x^2+y+z)^2-(w)^2}{x^2+y+z-w}\)

\(lt_{(x,y,z,w)\rightarrow(3,1,1,11)}\frac{(x^2+y+z+w).(x^2+y+z-w)}{x^2+y+z-w}\)

\(lt_{(x,y,z,w)\rightarrow(3,1,1,11)}(x^2+y+z+w)\)=(3^2+1+1+11)

=9+1+1+11=22